Subgroups — #28596972

Order 15104.

676 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21427394	C₂	1	1	yes	maximal, characteristic
2	#21424707	C₂	1	1	yes	maximal, characteristic
3	#21424700	C₂	1	1	yes	maximal, characteristic
4	#21424700	C₂	1	1	yes	maximal, characteristic
5	#21424658	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424651	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424651	C₂	1	1	yes	maximal, characteristic, complemented
8	#21423969	C₂	1	1	yes	maximal, characteristic, complemented
9	#21423962	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423957	C₂	1	1	yes	maximal, characteristic, complemented
11	#21423878	C₂	1	1	yes	maximal, characteristic
12	#21423878	C₂	1	1	yes	maximal, characteristic
13	#21423876	C₂	1	1	yes	maximal, characteristic
14	#21423783	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1840	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#11745659	C₂²	1	1	yes	characteristic
17	C₂×Dic₅₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×Dic₅₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×Dic₅₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×#14273638	C₂²	1	1	yes	characteristic
24	C₂×#14273638	C₂²	1	1	yes	characteristic
25	C₂×#14273638	C₂²	1	1	yes	characteristic
26	C₂×#14273637	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
32	C₅₉⋊#401	C₄	1	1	yes	characteristic
33	#16837343	C₄	1	1	yes	characteristic
34	#16837343	C₄	1	1	yes	characteristic
35	#16837343	C₄	1	1	yes	characteristic
36	#16837331	C₄	1	1	yes	characteristic
37	#16837331	C₄	1	1	yes	characteristic
38	#16837331	C₄	1	1	yes	characteristic
39	#16837326	C₄	1	1	yes	characteristic
40	C₄×Dic₅₉⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×Dic₅₉⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×Dic₅₉⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×(C₂×D₅₉)⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×(C₂×D₅₉)⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×(C₂×D₅₉)⋊C₄	C₂²	1	1	yes	characteristic
46	#16837156	C₂²	1	1	yes	characteristic
47	#16837156	C₂²	1	1	yes	characteristic
48	#16837156	C₂²	1	1	yes	characteristic
49	#16837156	C₂²	1	1	yes	characteristic
50	#16837156	C₂²	1	1	yes	characteristic
51	#16837156	C₂²	1	1	yes	characteristic
52	C₅₉×#376	C₂²	1	1	yes	characteristic
53	C₅₉×#336	C₂²	1	1	yes	characteristic
54	C₅₉×#336	C₂²	1	1	yes	characteristic
55	C₅₉×#336	C₂²	1	1	yes	characteristic
56	C₅₉×#336	C₂²	1	1	yes	characteristic
57	C₅₉×#336	C₂²	1	1	yes	characteristic
58	C₅₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₅₉	C₂³	1	1	yes	characteristic
60	C₂×#11745659	—	2	2	no	—
61	C₂×#11745659	—	2	2	no	—
62	C₂×#11745659	—	2	2	no	—
63	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
80	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
82	Dic₅₉⋊C₈	—	2	2	no	—
83	Dic₅₉⋊C₈	—	2	2	no	—
84	Dic₅₉⋊C₈	—	2	2	no	—
85	(C₂×D₅₉)⋊C₈	—	2	2	no	—
86	(C₂×D₅₉)⋊C₈	—	2	2	no	—
87	(C₂×D₅₉)⋊C₈	—	2	2	no	—
88	#14273638	—	2	2	no	—
89	#14273638	—	2	2	no	—
90	#14273638	—	2	2	no	—
91	#14273637	—	2	2	no	—
92	C₄×C₅₉⋊C₈	—	2	2	no	—
93	C₄×C₅₉⋊C₈	—	2	2	no	—
94	C₄×C₅₉⋊C₈	—	2	2	no	—
95	C₈×Dic₅₉	—	2	2	no	—
96	C₈×Dic₅₉	—	2	2	no	—
97	C₅₉⋊#95	C₂×C₄	1	1	yes	characteristic
98	C₅₉⋊#95	C₂×C₄	1	1	yes	characteristic
99	C₅₉⋊#95	C₂×C₄	1	1	yes	characteristic
100	C₅₉⋊#95	C₂×C₄	1	1	yes	characteristic
101	C₅₉⋊#95	C₂×C₄	1	1	yes	characteristic
102	C₅₉⋊#95	C₂×C₄	1	1	yes	characteristic
103	C₅₉⋊#95	C₂×C₄	1	1	yes	characteristic
104	C₅₉⋊#95	C₂×C₄	1	1	yes	characteristic
105	C₅₉⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₅₉⋊#95	C₂×C₄	1	1	yes	characteristic
107	C₅₉⋊#95	C₂×C₄	1	1	yes	characteristic
108	C₅₉⋊#95	C₂×C₄	1	1	yes	characteristic
109	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
116	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
117	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
118	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
119	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
120	C₂³×D₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
128	C₂²×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₅₉	—	2	1	no	—
136	C₂×C₄×D₅₉	—	2	1	no	—
137	C₂×C₄×D₅₉	—	2	1	no	—
138	C₂×C₄×D₅₉	—	2	1	no	—
139	C₂×C₄×D₅₉	—	2	1	no	—
140	C₂×C₄×D₅₉	—	2	1	no	—
141	C₂×C₈×C₅₉	—	2	1	no	—
142	C₂×C₈×C₅₉	—	2	1	no	—
143	C₂×C₈×C₅₉	—	2	1	no	—
144	C₂×C₈×C₅₉	—	2	1	no	—
145	C₂×C₈×C₅₉	—	2	1	no	—
146	C₂×C₈×C₅₉	—	2	1	no	—
147	C₂×C₈×C₅₉	—	2	1	no	—
148	C₂×C₈×C₅₉	—	2	1	no	—
149	C₂×C₈×C₅₉	—	2	1	no	—
150	C₂×C₈×C₅₉	—	2	1	no	—
151	C₂×C₈×C₅₉	—	2	1	no	—
152	C₂×C₈×C₅₉	—	2	1	no	—
153	C₄²×C₅₉	—	2	1	no	—
154	C₄²×C₅₉	—	2	1	no	—
155	C₄²×C₅₉	—	2	1	no	—
156	C₄²×C₅₉	—	2	1	no	—
157	C₄²×C₅₉	—	2	1	no	—
158	C₄²×C₅₉	—	2	1	no	—
159	(C₂×D₅₉)⋊C₄	—	2	2	no	—
160	(C₂×D₅₉)⋊C₄	—	2	2	no	—
161	(C₂×D₅₉)⋊C₄	—	4	1	no	—
162	(C₂×D₅₉)⋊C₄	—	4	1	no	—
163	(C₂×D₅₉)⋊C₄	—	4	1	no	—
164	(C₂×D₅₉)⋊C₄	—	4	1	no	—
165	Dic₅₉⋊C₄	—	2	2	no	—
166	Dic₅₉⋊C₄	—	2	2	no	—
167	Dic₅₉⋊C₄	—	2	2	no	—
168	Dic₅₉⋊C₄	—	2	2	no	—
169	Dic₅₉⋊C₄	—	4	1	no	—
170	Dic₅₉⋊C₄	—	4	1	no	—
171	C₄×Dic₅₉	—	2	1	no	—
172	C₄×Dic₅₉	—	2	1	no	—
173	C₄×Dic₅₉	—	2	1	no	—
174	C₄×Dic₅₉	—	2	1	no	—
175	C₄×Dic₅₉	—	2	1	no	—
176	C₄×Dic₅₉	—	2	1	no	—
177	C₂×C₅₉⋊C₈	—	2	1	no	—
178	C₂×C₅₉⋊C₈	—	2	1	no	—
179	C₂×C₅₉⋊C₈	—	2	1	no	—
180	C₂×C₅₉⋊C₈	—	2	1	no	—
181	C₂×C₅₉⋊C₈	—	2	1	no	—
182	C₂×C₅₉⋊C₈	—	2	1	no	—
183	C₂×C₅₉⋊C₈	#41	1	2	yes	—
184	C₂×C₅₉⋊C₈	#41	1	2	yes	—
185	C₂×C₅₉⋊C₈	#41	1	2	yes	—
186	C₂×C₅₉⋊C₈	#41	1	2	yes	—
187	C₂×C₅₉⋊C₈	#41	1	2	yes	—
188	C₂×C₅₉⋊C₈	#41	1	2	yes	—
189	#11745659	—	4	4	no	—
190	C₂³×C₅₉	C₂³×C₄	1	1	yes	characteristic
191	C₂²×D₅₉	—	2	1	no	—
192	C₂²×D₅₉	—	2	1	no	—
193	C₂²×D₅₉	—	2	1	no	—
194	C₂²×D₅₉	—	2	1	no	—
195	C₂²×D₅₉	—	2	1	no	—
196	C₂²×D₅₉	—	2	1	no	—
197	C₂²×D₅₉	—	2	1	no	—
198	C₂×C₄×C₅₉	—	2	1	no	—
199	C₂×C₄×C₅₉	—	2	1	no	—
200	C₂×C₄×C₅₉	—	2	1	no	—
201	C₂×C₄×C₅₉	—	2	1	no	—
202	C₂×C₄×C₅₉	—	2	1	no	—
203	C₂×C₄×C₅₉	—	2	1	no	—
204	C₂×C₄×C₅₉	—	2	1	no	—
205	C₂×C₄×C₅₉	—	2	1	no	—
206	C₂×C₄×C₅₉	—	2	1	no	—
207	C₂×C₄×C₅₉	—	2	1	no	—
208	C₂×C₄×C₅₉	—	2	1	no	—
209	C₂×C₄×C₅₉	—	2	1	no	—
210	C₂×C₄×C₅₉	—	2	1	no	—
211	C₂×C₄×C₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	2	1	no	—
213	C₂×C₄×C₅₉	—	2	1	no	—
214	C₂×C₄×C₅₉	—	2	1	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
222	C₂×Dic₅₉	—	2	1	no	—
223	C₂×Dic₅₉	—	2	1	no	—
224	C₂×Dic₅₉	—	2	1	no	—
225	C₂×Dic₅₉	—	2	1	no	—
226	C₂×Dic₅₉	—	2	1	no	—
227	C₂×Dic₅₉	—	2	1	no	—
228	C₂×Dic₅₉	—	2	1	no	—
229	C₂×Dic₅₉	—	2	1	no	—
230	C₂×Dic₅₉	—	2	1	no	—
231	C₂×Dic₅₉	—	2	1	no	—
232	C₂×Dic₅₉	—	2	1	no	—
233	C₂×Dic₅₉	—	2	1	no	—
234	C₂×Dic₅₉	—	2	1	no	—
235	C₂×Dic₅₉	—	2	1	no	—
236	C₂×Dic₅₉	—	2	1	no	—
237	C₂×Dic₅₉	—	2	1	no	—
238	C₂×Dic₅₉	—	2	1	no	—
239	C₂×Dic₅₉	—	2	1	no	—
240	C₂×Dic₅₉	—	2	1	no	—
241	C₂×Dic₅₉	#131	1	2	yes	—
242	C₂×Dic₅₉	#131	1	2	yes	—
243	C₄×D₅₉	—	4	1	no	—
244	C₄×D₅₉	—	4	1	no	—
245	C₄×D₅₉	—	4	1	no	—
246	C₄×D₅₉	—	4	1	no	—
247	C₈×C₅₉	—	4	1	no	—
248	C₈×C₅₉	—	4	1	no	—
249	C₈×C₅₉	—	4	1	no	—
250	C₈×C₅₉	—	4	1	no	—
251	C₅₉⋊C₈	—	2	2	no	—
252	C₅₉⋊C₈	—	2	2	no	—
253	C₅₉⋊C₈	—	2	2	no	—
254	C₅₉⋊C₈	#126	1	4	yes	—
255	#21671	—	59	1	no	maximal, Sylow
256	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
257	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
258	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
259	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
260	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
261	C₂²×C₅₉	#568	1	1	yes	characteristic
262	C₂²×C₅₉	#568	1	1	yes	characteristic
263	C₂×D₅₉	—	4	1	no	—
264	C₂×D₅₉	—	4	1	no	—
265	C₂×D₅₉	—	4	1	no	—
266	C₂×D₅₉	—	4	1	no	—
267	C₂×D₅₉	—	4	1	no	—
268	C₂×D₅₉	—	4	1	no	—
269	C₂×D₅₉	—	4	1	no	—
270	C₄×C₅₉	—	4	1	no	—
271	C₄×C₅₉	—	4	1	no	—
272	C₄×C₅₉	—	4	1	no	—
273	C₄×C₅₉	—	4	1	no	—
274	C₄×C₅₉	—	4	1	no	—
275	C₄×C₅₉	—	4	1	no	—
276	C₄×C₅₉	C₂×#126	1	1	yes	characteristic
277	C₄×C₅₉	#529	1	1	yes	characteristic
278	C₄×C₅₉	#529	1	1	yes	characteristic
279	C₄×C₅₉	#529	1	1	yes	characteristic
280	Dic₅₉	—	2	2	no	—
281	Dic₅₉	—	2	2	no	—
282	Dic₅₉	—	4	1	no	—
283	Dic₅₉	—	4	1	no	—
284	Dic₅₉	—	4	1	no	—
285	Dic₅₉	—	4	1	no	—
286	Dic₅₉	—	4	1	no	—
287	#2401	—	59	1	no	—
288	#1924	—	59	1	no	—
289	#1923	—	59	1	no	—
290	#1923	—	59	1	no	—
291	#1917	—	59	1	no	—
292	#1916	—	59	1	no	—
293	#1916	—	59	1	no	—
294	#1840	D₅₉	1	1	yes	characteristic, complemented
295	#1771	—	59	1	no	—
296	#1770	—	59	1	no	—
297	C₈×C₄⋊C₄	—	59	1	no	—
298	#1753	—	59	1	no	—
299	#1753	—	59	1	no	—
300	#1753	—	59	1	no	—
301	#1726	—	59	1	no	—
302	C₂×C₅₉	C₄×#126	1	1	yes	characteristic
303	C₂×C₅₉	#2966	1	1	yes	characteristic
304	C₂×C₅₉	#2967	1	1	yes	characteristic
305	C₂×C₅₉	#2968	1	1	yes	characteristic
306	C₂×C₅₉	#2969	1	1	yes	characteristic
307	C₂×C₅₉	#2969	1	1	yes	characteristic
308	C₂×C₅₉	#2969	1	1	yes	characteristic
309	D₅₉	—	8	1	no	—
310	C₂²×M₁₆	—	59	1	no	—
311	C₂×C₄⋊C₈	—	59	1	no	—
312	C₂×C₄⋊C₈	—	59	1	no	—
313	C₂×C₄⋊C₈	—	59	1	no	—
314	C₂×C₂²⋊C₈	—	59	1	no	—
315	C₂×C₂²⋊C₈	—	59	1	no	—
316	C₂×C₂²⋊C₈	—	59	1	no	—
317	C₂×#97	—	59	1	no	—
318	C₂×#97	—	59	1	no	—
319	C₂×#97	—	59	1	no	—
320	C₂×#97	—	59	1	no	—
321	C₂×C₄×C₈	—	59	1	no	—
322	C₂×C₄×C₈	—	59	1	no	—
323	C₂×C₄×C₈	—	59	1	no	—
324	C₂×C₄×C₈	—	59	1	no	—
325	C₂×C₄×C₈	—	59	1	no	—
326	#401	—	59	1	no	—
327	#400	—	59	1	no	—
328	#400	—	59	1	no	—
329	#400	—	59	1	no	—
330	#397	—	59	1	no	—
331	#397	—	59	1	no	—
332	#397	—	59	1	no	—
333	#396	—	59	1	no	—
334	C₄×C₄⋊C₄	—	59	1	no	—
335	C₄×C₄⋊C₄	—	59	1	no	—
336	C₄×C₄⋊C₄	—	59	1	no	—
337	C₄×C₂²⋊C₄	—	59	1	no	—
338	C₄×C₂²⋊C₄	—	59	1	no	—
339	C₄×C₂²⋊C₄	—	59	1	no	—
340	#376	C₂×D₅₉	1	1	yes	characteristic
341	#336	—	59	1	no	—
342	#336	—	59	1	no	—
343	#336	—	59	1	no	—
344	#336	—	59	1	no	—
345	#336	—	59	1	no	—
346	#336	—	59	1	no	—
347	#336	C₂×D₅₉	1	1	yes	characteristic
348	#336	C₂×D₅₉	1	1	yes	characteristic
349	#336	C₂×D₅₉	1	1	yes	characteristic
350	#336	C₂×D₅₉	1	1	yes	characteristic
351	#336	C₂×D₅₉	1	1	yes	characteristic
352	#336	C₂×D₅₉	1	1	yes	characteristic
353	C₅₉	#21671	1	1	yes	characteristic, complemented, Sylow
354	C₂³×C₄	—	59	1	no	—
355	C₂×M₁₆	—	118	2	no	—
356	C₂×M₁₆	—	118	2	no	—
357	C₂×M₁₆	—	118	2	no	—
358	C₂²×C₈	—	59	1	no	—
359	C₂²×C₈	—	59	1	no	—
360	C₂²×C₈	—	59	1	no	—
361	C₂²×C₈	—	59	1	no	—
362	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
363	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
364	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
365	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
366	C₂×C₄⋊C₄	—	59	1	no	—
367	C₂×C₄⋊C₄	—	59	1	no	—
368	C₂×C₄⋊C₄	—	59	1	no	—
369	C₂×C₄⋊C₄	—	59	1	no	—
370	C₂×C₄⋊C₄	—	59	1	no	—
371	C₂×C₄⋊C₄	—	59	1	no	—
372	C₂×C₂²⋊C₄	—	59	1	no	—
373	C₂×C₂²⋊C₄	—	59	1	no	—
374	C₂×C₂²⋊C₄	—	59	1	no	—
375	C₂×C₂²⋊C₄	—	59	1	no	—
376	C₂×C₂²⋊C₄	—	59	1	no	—
377	C₂×C₂²⋊C₄	—	59	1	no	—
378	C₂×C₄²	—	59	1	no	—
379	C₂×C₄²	—	59	1	no	—
380	C₂×C₄²	—	59	1	no	—
381	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
382	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
383	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
384	C₄⋊C₈	—	118	2	no	—
385	C₄⋊C₈	—	118	2	no	—
386	C₄⋊C₈	—	118	2	no	—
387	C₂²⋊C₈	—	118	2	no	—
388	C₂²⋊C₈	—	118	2	no	—
389	C₂²⋊C₈	—	118	2	no	—
390	#97	—	118	2	no	—
391	#97	—	118	2	no	—
392	#97	—	118	2	no	—
393	#97	—	118	2	no	—
394	C₄×C₈	—	118	2	no	—
395	C₄×C₈	—	118	2	no	—
396	C₄×C₈	—	118	2	no	—
397	C₄×C₈	—	118	2	no	—
398	C₄×C₈	—	118	2	no	—
399	#95	—	59	1	no	—
400	#95	—	59	1	no	—
401	#95	—	59	1	no	—
402	#95	—	59	1	no	—
403	#95	—	59	1	no	—
404	#95	—	59	1	no	—
405	#95	—	59	1	no	—
406	#95	—	59	1	no	—
407	#95	—	59	1	no	—
408	#95	—	59	1	no	—
409	#95	—	59	1	no	—
410	#95	—	59	1	no	—
411	#95	C₄×D₅₉	1	1	yes	characteristic
412	#95	C₄×D₅₉	1	1	yes	characteristic
413	#95	C₄×D₅₉	1	1	yes	characteristic
414	#95	C₄×D₅₉	1	1	yes	characteristic
415	C₂⁴	—	59	1	no	—
416	C₂²×C₄	—	59	1	no	—
417	C₂²×C₄	—	59	1	no	—
418	C₂²×C₄	—	59	1	no	—
419	C₂²×C₄	—	59	1	no	—
420	C₂²×C₄	—	59	1	no	—
421	C₂²×C₄	—	59	1	no	—
422	C₂²×C₄	—	59	1	no	—
423	C₂²×C₄	—	118	1	no	—
424	C₂²×C₄	—	118	1	no	—
425	C₂²×C₄	—	118	1	no	—
426	C₂²×C₄	—	118	1	no	—
427	C₂²×C₄	—	118	1	no	—
428	C₂²×C₄	—	118	1	no	—
429	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
435	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
436	M₁₆	—	236	4	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	59	2	no	—
450	C₂×C₈	—	59	2	no	—
451	C₂×C₈	—	59	2	no	—
452	C₂×C₈	—	59	2	no	—
453	C₂×C₈	—	59	2	no	—
454	C₂×C₈	—	59	2	no	—
455	C₂×C₈	—	118	1	no	—
456	C₂×C₈	—	118	1	no	—
457	C₂×C₈	—	118	1	no	—
458	C₂×C₈	—	118	1	no	—
459	C₂×C₈	—	118	1	no	—
460	C₂×C₈	—	118	1	no	—
461	C₄⋊C₄	—	118	2	no	—
462	C₄⋊C₄	—	118	2	no	—
463	C₄⋊C₄	—	118	2	no	—
464	C₄⋊C₄	—	118	2	no	—
465	C₄⋊C₄	—	236	1	no	—
466	C₄⋊C₄	—	236	1	no	—
467	C₂²⋊C₄	—	118	2	no	—
468	C₂²⋊C₄	—	118	2	no	—
469	C₂²⋊C₄	—	236	1	no	—
470	C₂²⋊C₄	—	236	1	no	—
471	C₂²⋊C₄	—	236	1	no	—
472	C₂²⋊C₄	—	236	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	118	1	no	—
480	C₄²	—	118	1	no	—
481	C₄²	—	118	1	no	—
482	C₄²	—	118	1	no	—
483	C₄²	—	118	1	no	—
484	C₄²	—	118	1	no	—
485	C₂³	—	118	1	no	—
486	C₂³	—	118	1	no	—
487	C₂³	—	118	1	no	—
488	C₂³	—	118	1	no	—
489	C₂³	—	118	1	no	—
490	C₂³	—	118	1	no	—
491	C₂³	—	118	1	no	—
492	C₂³	C₂²×C₄×D₅₉	1	1	yes	characteristic
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	59	2	no	—
512	C₂×C₄	—	59	2	no	—
513	C₂×C₄	—	118	1	no	—
514	C₂×C₄	—	118	1	no	—
515	C₂×C₄	—	118	1	no	—
516	C₂×C₄	—	118	1	no	—
517	C₂×C₄	—	118	1	no	—
518	C₂×C₄	—	118	1	no	—
519	C₂×C₄	—	118	1	no	—
520	C₂×C₄	—	118	1	no	—
521	C₂×C₄	—	118	1	no	—
522	C₂×C₄	—	118	1	no	—
523	C₂×C₄	—	118	1	no	—
524	C₂×C₄	—	118	1	no	—
525	C₂×C₄	—	118	1	no	—
526	C₂×C₄	—	118	1	no	—
527	C₂×C₄	—	118	1	no	—
528	C₂×C₄	—	118	1	no	—
529	C₂×C₄	—	118	1	no	—
530	C₂×C₄	—	118	1	no	—
531	C₂×C₄	—	118	1	no	—
532	C₂×C₄	—	236	1	no	—
533	C₂×C₄	—	236	1	no	—
534	C₂×C₄	—	236	1	no	—
535	C₂×C₄	—	236	1	no	—
536	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
537	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
538	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
539	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
540	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
541	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	59	4	no	—
547	C₈	—	118	2	no	—
548	C₈	—	118	2	no	—
549	C₈	—	118	2	no	—
550	C₂²	—	236	1	no	—
551	C₂²	—	236	1	no	—
552	C₂²	—	236	1	no	—
553	C₂²	—	236	1	no	—
554	C₂²	—	236	1	no	—
555	C₂²	—	236	1	no	—
556	C₂²	—	236	1	no	—
557	C₂²	#16837870	1	1	yes	characteristic
558	C₂²	#16837870	1	1	yes	characteristic
559	C₂²	#16837870	1	1	yes	characteristic
560	C₂²	#131×D₅₉	1	1	yes	characteristic
561	C₂²	#131×D₅₉	1	1	yes	characteristic
562	C₂²	#16838167	1	1	yes	characteristic
563	C₂²	#16838167	1	1	yes	characteristic
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	118	2	no	—
571	C₄	—	118	2	no	—
572	C₄	—	236	1	no	—
573	C₄	—	236	1	no	—
574	C₄	—	236	1	no	—
575	C₄	—	236	1	no	—
576	C₄	—	236	1	no	—
577	C₄	#126×D₅₉	1	1	yes	characteristic
578	C₄	#16837935	1	1	yes	characteristic
579	C₄	#16837935	1	1	yes	characteristic
580	C₄	#16837935	1	1	yes	characteristic
581	C₂	—	472	1	no	—
582	C₂	#21426644	1	1	yes	characteristic
583	C₂	#21433069	1	1	yes	characteristic
584	C₂	#21433079	1	1	yes	characteristic
585	C₂	#21433088	1	1	yes	characteristic
586	C₂	#21433098	1	1	yes	characteristic
587	C₂	#21433098	1	1	yes	characteristic
588	C₂	#21433098	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂³×C₄
Fitting	C₅₉×#1840	C₂
prime radical	C₂³×D₅₉	C₂²×C₄
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1840	D₅₉
hypocenter	C₅₉	#21671
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1840

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. #21424658	C₂	semidirect
6. #21424651	C₂	semidirect
7. #21424651	C₂	semidirect
8. #21423969	C₂	semidirect
9. #21423962	C₂	semidirect
10. #21423957	C₂	semidirect
14. #21423783	C₂	semidirect
15. C₅₉×#1840	C₂	semidirect
294. #1840	D₅₉	semidirect
353. C₅₉	#21671	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#21427394	2
#21424707	2
#21424700	2
#21424658	2
#21424651	2
#21423969	2
#21423962	2
#21423957	2
#21423878	2
#21423876	2
#21423783	2
C₅₉×#1840	2
#21671	59